IB Mathematics AA HL Flashcards- More Rational Functions

We have seen functions in the form: \( f(x) = \frac{ax + b}{cx + d} \), in section 2.8. Now, we deal with \( f(x) = \frac{ax^2 + bx + c}{cx^2 + dx + e} \) & \( f(x) = \frac{ax^2 + bx + c}{dx + e} \).

We saw vertical/horizontal asymptotes previously, but whenever the degree of the numerator is greater than the denominator (as it is here), we may see an oblique (diagonal) asymptote

[q] 

As \( x \to \infty \), the denominator rises much faster, so the H.A. is always at \( y = 0 \). If you solve the denominator \( = 0 \), you get any potential vertical asymptotes. Solve \( ax + b = 0 \) for x-ints, and y-int is at \( (0, \frac{b}{e}) \). Finally, plug in values just above or below V.A.’s to help with the shape:

[x] Exit text